Matrix

Matrix

A matrix is a rectangular arrangement of numbers written in rows and columns. The numbers are enclosed in square brackets [ ] or parentheses ( ). A matrix is usually denoted by capital letters of the English alphabet, while its elements are represented by small letters. It is simply a way of representing data and does not have any quantitative value by itself.

Order of a Matrix

The order of a matrix tells us how many rows and columns it has. It is written as m × n.

m = number of rows             n = number of columns

👉 Example:

$$A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}$$

This matrix has 2 rows and 3 columns, so its order is 2 × 3.

Positions of Elements of a Matrix

Every number in a matrix is called an element, and each element has a position.

- The element in the $i^{th}$ row and $j^{th}$ column is written as $a_{ij}$.

👉 Example:

$$B = \begin{bmatrix} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{bmatrix}$$

- $a_{12} = 8$ (row 1, column 2)              $a_{31} = 11$ (row 3, column 1)

So, the position helps us identify each element inside a matrix.